Convergence of one-dimensional diffusion processes to a jump process related to population genetics

✍ Scribed by Masaru Iizukah; Yukio Ogura

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 865 KB
• Volume: 29
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00163918

✦ Synopsis

A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits; strong selection-weak mutation limit, moderate selection-weak mutation limit, weak selection-weak mutation limit are considered for typical diffusion models in population genetics.